An algebraic characterization of holomorphic nondegeneracy for real algebraic hypersurfaces and its application to CR mappings

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Abstract

We give a new algebraic characterization of holomorphic nondegeneracy for embedded real algebraic hypersurfaces in ℂN+1, N ≥ 1. We then use this criterion to prove the following result about real analyticity of smooth CR mappings : any smooth CR mapping H between a real analytic hypersurface and a rigid polynomial holomorphically nondegenerate hypersurface is real analytic, provided the map H is not totally degenerate in the sense of Baouendi and Rothschild.

Original languageEnglish
Pages (from-to)189-202
Number of pages14
JournalMathematische Zeitschrift
Volume231
Issue number1
Publication statusPublished - May 1999
Externally publishedYes

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CR Mappings
Nondegeneracy
Hypersurface
Analyticity
Polynomial

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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abstract = "We give a new algebraic characterization of holomorphic nondegeneracy for embedded real algebraic hypersurfaces in ℂN+1, N ≥ 1. We then use this criterion to prove the following result about real analyticity of smooth CR mappings : any smooth CR mapping H between a real analytic hypersurface and a rigid polynomial holomorphically nondegenerate hypersurface is real analytic, provided the map H is not totally degenerate in the sense of Baouendi and Rothschild.",
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